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Unformatted text preview: CS2022 Test #1 Friday, November 5, 2004 150 Points #1. (30 points) Let h = “John is healthy” w = “John is wealthy” s = “John is wise” Write statements in symbolic form using h, w, and s and the appropriate logical connectives for each of the following: a) John is healthy, wealthy, but not wise (h ∧ w) ∧ ~s b) John is neither wealthy nor wise, but he is healthy (~w ∧ ~s) ∧ h or ~(w ∨ s) ∧ h c) John is wealthy, but he is not both healthy and wise w ∧ ~( h ∧ s) Note: Some people saw the “not both” and immediately thought “XOR”. But XOR has 2 parts: 1) One of the two choices has to be true (that’s not the case here) and 2) Not both are true. 2. (20 points) Let R(x): “x is a rational number” I(x): “x is an integer” Express “All integers are rational numbers, but some rational numbers are not integers” using Ratl(x), Int(x), quantifiers and logical connectives 2200 x (Int(x) Ratl(x)) ∧ 5 x (Ratl(x) ∧ ~Int(x)) #3. (40 points) Which of the following implications are true? Justify your answer.#3....
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 Spring '08
 WOUTERS
 Logic, Algebra, Rational number, odd integers

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